Algebra Examples

$\frac{b}{a^{2}} = 16$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$a^{2}, 1$

Step 1.2

The LCM of one and any expression is the expression.

$a^{2}$

Step 2

Multiply each term in $\frac{b}{a^{2}} = 16$ by $a^{2}$ to eliminate the fractions.

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Step 2.1

Multiply each term in $\frac{b}{a^{2}} = 16$ by $a^{2}$ .

$\frac{b}{a^{2}} a^{2} = 16 a^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $a^{2}$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{b}{a^{2}} a^{2} = 16 a^{2}$

Step 2.2.1.2

Rewrite the expression.

$b = 16 a^{2}$

Step 3

Solve the equation.

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Step 3.1

Rewrite the equation as $16 a^{2} = b$ .

$16 a^{2} = b$

Step 3.2

Divide each term in $16 a^{2} = b$ by $16$ and simplify.

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Step 3.2.1

Divide each term in $16 a^{2} = b$ by $16$ .

$\frac{16 a^{2}}{16} = \frac{b}{16}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $16$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{16 a^{2}}{16} = \frac{b}{16}$

Step 3.2.2.1.2

Divide $a^{2}$ by $1$ .

$a^{2} = \frac{b}{16}$

Step 3.3

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$a = \pm \sqrt{\frac{b}{16}}$

Step 3.4

Simplify $\pm \sqrt{\frac{b}{16}}$ .

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Step 3.4.1

Rewrite $\frac{b}{16}$ as ${(\frac{1}{4})}^{2} b$ .

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Step 3.4.1.1

Factor the perfect power $1^{2}$ out of $b$ .

$a = \pm \sqrt{\frac{1^{2} b}{16}}$

Step 3.4.1.2

Factor the perfect power $4^{2}$ out of $16$ .

$a = \pm \sqrt{\frac{1^{2} b}{4^{2} \cdot 1}}$

Step 3.4.1.3

Rearrange the fraction $\frac{1^{2} b}{4^{2} \cdot 1}$ .

$a = \pm \sqrt{{(\frac{1}{4})}^{2} b}$

Step 3.4.2

Pull terms out from under the radical.

$a = \pm \frac{1}{4} \sqrt{b}$

Step 3.4.3

Combine $\frac{1}{4}$ and $\sqrt{b}$ .

$a = \pm \frac{\sqrt{b}}{4}$

Step 3.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.5.1

First, use the positive value of the $\pm$ to find the first solution.

$a = \frac{\sqrt{b}}{4}$

Step 3.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$a = - \frac{\sqrt{b}}{4}$

Step 3.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$a = \frac{\sqrt{b}}{4}$

$a = - \frac{\sqrt{b}}{4}$

$a = \frac{\sqrt{b}}{4}$

$a = - \frac{\sqrt{b}}{4}$

$a = \frac{\sqrt{b}}{4}$

$a = - \frac{\sqrt{b}}{4}$